Which expression is equivalent to the following complex fraction? StartFraction 2 Over x EndFraction minus StartFraction 4 Over y EndFraction divided by StartFraction negative 5 Over y EndFraction + StartFraction 3 Over x EndFraction StartFraction 3 y + 5 x Over 2 (y minus 2 x) EndFraction StartFraction 2 (y minus 2 x) Over 3 y minus 5 x EndFraction StartFraction 2 (y minus 2 x) (3 y minus 5 x) Over x squared y squared EndFraction StartFraction x squared y squared Over 2 (y minus 2 x) (3 y minus 5 x) EndFraction

Answer:

to find domain just take the first values of each ordered pairs

to find the range just take the second values of each ordered pairs.

If we know the concepts of transformations and horizontal translation and that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).

The transformation of functions are operations which modify the relationship between input and outputs in a function. The parent function represents a canonical square root function and the transformed function is the consequence of applying a horizontal translation.

This kind of transformation is defined by the following expression:

g(x) = f(x - k)     (1)

Where k represents a rightward translation for k > 0.

If we know that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).

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Answer: x=-1 and y=-2

The values of x and y by the descriptions in the task content are; 7.5 and 9 respectively.

It follows from the task content that the description in the task content registers the bottom right angle measure of the second intersection as equal to 10y.

Hence, it follows that; 10y = 90 and; y = 9.

From the first intersection; 6x + 5y = 90;

6x + 5(9) = 90

6x + 45 = 90

6x = 45

x = 45/6 = 7.5

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-10 belongs to the set of negative integers and rational numbers and also belongs to the set of real numbers.

The amount of waste is 22 oz

The weights of the 3 rainbow trouts are:

3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz.

The total weight is:

Total = 3 Ib 5 oz + 2 Ib 12 oz + 3 Ib 8 oz

Evaluate the sum

Total = 8 Ib 25 oz

The amount she was left with is 8 Ib 2 oz

Subtract this amount from the total

Waste = 8 Ib 25 oz - 8 Ib 2 oz

Evaluate

Waste = 22 oz

Hence, the amount of waste is 22 oz

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A horizontal translation of the function by 4 units and a vertical translation down by 3 units

The parent function of the given function is g(x) = |x|. The resulting function (x) = | 2x − 4 | − 3 shows the following translations

A vertical stretch of the graph by 2 units

A horizontal translation of the function by 4 units and a vertical translation down by 3 units

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There are 9240 ways to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department.

It is given that there are 9 faculty members in the math department and 11 in the computer science department.

[tex]C^{9} _{3} * C^{11} _{4}[/tex]

[tex]= \frac{9!}{(9-3)!3!} * \frac{11!}{(11-4)!4!}\\= 28 * 330\\= 9240[/tex]

Therefore, there are 9240 ways to select the committee.

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Answer:

2nd option

Step-by-step explanation:

the quadrilateral has 1 pair of parallel sides and is therefore a trapezoid.

• each lower base angle is supplementary to the upper base angle on the same side, that is

∠ 1 + ∠ 2 = 180° , so

x + x + 50 = 180

2x + 50 = 180 ( subtract 50 from both sides )

2x = 130 ( divide both sides by 2 )

x = 65

then

∠ 1 = x = 65°

∠ 2 = x + 50 = 65 + 50 = 115°

Answer: 140°

Step-by-step explanation:

- all straight lines are 180°

- since ACD and DCB help to create the straight line they must equal 180° when combined

- so 180 - 40 = 140

- therefore, ACD is 40° and DCB is 140°

hope this helps :)

The surface area of the cylinder is 244. 92 inches²

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 6 / 2 = 3 inches

h = 10 inches

surface area of a cylinder =  2 × 3.14 × 3(3 + 10)

surface area of a cylinder = 18.84(13)

surface area of a cylinder = 244.92

surface area of a cylinder = 244. 92 inches²

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Answer:

1 9/20x or 29/20x

Step-by-step explanation:

Reorder so it can be seen better

5x-4x+1/5x+1/4x

Combine like terms

x+1/5x+1/4x

Common multiple

x+4/20x+5/20x

Combine like terms

9/20x+x

Finalize

29/20x

Simplified

1 9/20x

Answer: -1/20x

Step-by-step explanation:

got all 5 correct this one was one of my five

The area of the deck is 413 square feet

Start by calculating the area of the outer rectangle using:

Area = Length * Width

This gives

Area1 = (18 + 12) * (16 + 8)

Area1 = 720

Next, calculate the area of the inner rectangle using:

Area = Length * Width

This gives

Area2 = 16 * (18 + 8)

Area2 = 416

Subtract these areas

A1 = Area1 - Area2

A1 = 720 - 416

A1 = 304

Next, calculate the area of the outer semicircle using:

Area = 0.5πR²

This gives

Area1 = 0.5 * 3 * (12-1)²

Area1 = 181.5

Next, calculate the area of the inner semicircle using:

Area = 0.5πr²

This gives

Area2 = 0.5 * 3 * (7)²

Area2 = 73.5

Subtract these areas

A2 = Area1 - Area2

A2 = 181.5 - 73.5

A2 = 108

Add A1 and A2

A = 304 + 108

Evaluate the sum

A = 412

Hence, the area of the deck is 413 square feet

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Answer:

40 total students

Explanation:

Total students: 100%

Let the number of total students be x.

Solving stepwise:

7.5% : 100% --> 3 : x

[tex]\rightarrow \sf \dfrac{7.5}{100} = \dfrac{3}{x}[/tex]

[tex]\rightarrow \sf 7.5x = 3(100)[/tex]

[tex]\rightarrow \sf 7.5x = 300[/tex]

[tex]\rightarrow \sf x =40[/tex]

Answer:

50 points

Step-by-step explanation:

Let the total points scored by the team = x

30% of x = 15 points

     [tex]\sf \dfrac{30}{100}*x = 15\\\\[/tex]

              [tex]\sf x = 15* \dfrac{100}{30}\\\\ x = 50[/tex]

The team scored 50 points.

The volume of the rectangular prism is 3359232 cubic centimeters

The length of the cube is given as:

Length, l = 12 cm

The volume of a cube is:

[tex]V = l^3[/tex]

So, we have:

[tex]V = 12^3[/tex]

Evaluate

V = 1728

The volume of 1944 cubes is then calculated as:

Volume = 1728 * 1944

Evaluate

Volume = 3359232

Hence, the volume of the rectangular prism is 3359232 cubic centimeters

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There are exactly 1,944 of the 12 cm, or 0.5 foot cubes inside a rectangular prism.  What is the volume of the rectangular prism in cubic centimeters?

The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Ultimately, since the dilation factor is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6 units.

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Answer: OPTION C

Step-by-step explanation:

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A, BC < MN.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

As per the given conditions, the angle that will be opposite to ∠A is BC and  ∠L is MN.

Now since the measure of ∠L is more than the measure of ∠A, therefore, the side MN will be greater than BC.

Hence, the correct option is A, BC < MN.

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Answer: Option 1 or A. BC<MN

Step-by-step explanation: Trust Me!

The answer is correct on Edge.  The proof is in the pic below.

Goodluck everyone! :)

Given AC = LN and BA = ML, which statement must be true?

A. BC < MN

Answer:

40 Including membership Price

35 Just for Pizza

Step-by-step explanation:

$5 for Membership for the month (Not sure if the final answer includes this or not)
1.75 x 20 = $35 for Pizza

The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C

It is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.

Thus, we have

RT/TQ = RV/VS

RT = x + 10

TQ = x - 3

RV = x + 10

VS = x

Substitute the value

[tex]\frac{x + 4}{x-3} = \frac{x + 10}{x}[/tex]
Cross multiply

(x+ 4) × x = (x + 10) × (x-3)

x² + 4x =  x² -3x + 10x -30

Divide through by x²

4x = -3x + 10x - 30

Collect like terms

4x + 3x - 10x = - 30

-3x = -30

x = -30/ -3

x = 10

Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C

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Answer: 8/15, 15/8

Step-by-step explanation:

By the Pythagorean theorem, the length of the unknown side is

[tex]\sqrt{17^{2}-8^{2}}=15[/tex]

So, the tangents of the acute angles are [tex]\boxed{\frac{8}{15}, \frac{15}{8}}[/tex]

Answer:

the answer is x= 3/4 I think

Step-by-step explanation:

6+8-90+90008-70000000

The number of watches that just be sold is 90 and the profit is -356400.

From the information given, the equation is given as:

P = −50x² + 550x − 900

P = -5x² + 55x - 90

= -5x² + 45x + 10x - 90

= -5x(x - 9) + 10(x - 9)

= (-5x + 10)(x - 9)

x - 9 = 0

x = 0 + 9 = 9

The watches that must be sold will be (9 × 10) = 90

The profit will be:

P = −50x² + 550x − 900

P = -50(90)² + 550(90) - 900

P = -405000 + 49500 - 900

P = -356400

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Using the arc length formula, the length of ST in the circle is: 15 units.

Arc length of a circle = ∅/360 × 2πr.

In the image given, we have:

∅ = m∠TSU = 72º

Arc length TU = 6π

r = ST

Plug in the values

6π = 72/360 × 2π(ST)

6π = 0.2 × 2π(ST)

6π/2π = 0.2 × ST

3 = 0.2(ST)

3/0.2 = ST

ST = 15 units.

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El cuadrado completo es:

[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]

Tenemos el cuadrado:

[tex]\left[\begin{array}{ccc}0.048&a&0.016\\b&c&0.072\\0.064&e&f\end{array}\right][/tex]

Y queremos encontrar los valores de las letras, tal que cada suma de columna, fila y de cada diagonal de 0.12,

Entonces tenemos:

0.048 + b + 0.064 = 0.12

b = 0.12 - 0.048 - 0.064 = 0.008

0.016 + 0.072 + f = 0.12

f = 0.12 - 0.016 - 0.072 = 0.032

Tambien las diagonales deben dar 0.12, entonces:

0.064 + c + 0.016 = 0.12

c = 0.12 - 0.016 - 0.064 = 0.04

Reemplazando esos valores obtenemos:

[tex]\left[\begin{array}{ccc}0.048&a&0.016\\0.008&0.04&0.072\\0.064&e&0.032\end{array}\right][/tex]

Ahora las filas tambien deben dar 0.12:

0.048 + a + 0.016 = 0.12

a = 0.12 - 0.048 - 0.016 = 0.056

0.064 + e + 0.032 = 0.12

e = 0.12 - 0.064 - 0.032 = 0.024

El cuadrado completo es:

[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]

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All possible lengths of segment AB wil be 27 < AB < 81.Option b is correct

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

Any two triangle sides' lengths added together are longer than the third side's length.

The triangular inequality theorem is applied in three ways;

1.

AC+BC > AB

27+54 > AB

81 > AB

2.

27+AB > 54

AB> 54-27

AB > -27

3.

54+AB > 27

AB > 27-54

AB > -27

All possible lengths of segment AB wil be 27 < AB < 81.

Hence option b is correct

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Answer:

27 < AB < 81

Step-by-step explanation:

The answer above is correct.

Vial contains 0.96g powder.

Proportion is used to show how quantities and amounts are related to each other. The amount that quantities change in relation to each other is governed by proportion rules.

A direct and inverse proportion are used to show how the quantities and amount are related to each other. They are also mentioned as directly proportional or inversely proportional. The symbol used to denote the proportionality is ‘∝‘.  For example, if we say, a is proportional to b, then it is represented as “a ∝ b” and if we say, a is inversely proportional to b, then it is denoted as ‘a∝1/b’

The given question is the example of direct variation.

Powder volume ∝ Liquid volume

∴ We can apply cross multiplication method

Let powder volume be x

1g→ 10ml

x→ 9.6ml

cross multiplying

1 x 9.6 = 10 x [tex]x[/tex]

x = 0.96 g

Thus Vial contains 0.96g powder.

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Answer:

[tex]y = 4 \cos(4\pi \: t + \frac{\pi}{4} ) [/tex]

[tex]y = a\cos(w\: t + \alpha ) [/tex]

[tex]w = 4\pi[/tex]

[tex]2\pi \: f = 4\pi[/tex]

[tex]f = 2[/tex]

Answer:

[tex]\displaystyle 2[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D[/tex]

When working with a trigonometric equation like this, always remember the information below:

[tex]\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]

So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:

[tex]\displaystyle \boxed{\frac{1}{2}} = \frac{2}{4\pi}\pi[/tex]

You will then plug this into the frequency formula, [tex]\displaystyle T^{-1} = F.[/tex] Look below:

[tex]\displaystyle \frac{1}{2}^{-1} = F \\ \\ \boxed{2 = F}[/tex]

Therefore, the frequency of motion is two hertz.

I am delighted to assist you at any time.